Problem: Simplify to lowest terms. $\dfrac{30}{18}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 18? $30 = 2\cdot3\cdot5$ $18 = 2\cdot3\cdot3$ $\mbox{GCD}(30, 18) = 2\cdot3 = 6$ $\dfrac{30}{18} = \dfrac{5 \cdot 6}{ 3\cdot 6}$ $\hphantom{\dfrac{30}{18}} = \dfrac{5}{3} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{30}{18}} = \dfrac{5}{3} \cdot 1$ $\hphantom{\dfrac{30}{18}} = \dfrac{5}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{18}= \dfrac{2\cdot15}{2\cdot9}= \dfrac{2\cdot 3\cdot5}{2\cdot 3\cdot3}= \dfrac{5}{3}$